Question: Expand and combine like terms. $(4+7a^2)^2=$
Solution: We can expand this expression using the "perfect square" pattern (where $P$ and $Q$ can be any monomial): $(P+Q)^2=P^2+2PQ+Q^2$ $\begin{aligned} &\phantom{=}\left(4+7a^2\right)^2 \\\\ &=\left(4\right)^2+2\left(4\right)\left(7a^2\right)+\left(7a^2\right)^2 \\\\ &=16+56a^2+49a^4 \\\\ &=49a^4+56a^2+16 \end{aligned}$